Can you find out what kind of math text/curriculum they are using? Can you
get a look at their books? This might give you an idea of what is going on
at the school.
Since you don't have much information, I would suggest you choose a topic
that reflects a high school level course and emphasizes your strengths.
Here's what I would be thinking about...
Most panels for whom I have done a demo lesson or of which I have been a
member have non-math educators as well as a math teacher. Each person looks
at you with a slightly different set of eyes and backgrounds in mathematics--
that different from my classroom. (We don't have honors Algebra 1 nor
honors Geometry. So my classes are have a range of abilities and
backgrounds.)
In all of my lessons, demo or real, I like to get my students involved, I do
a lot of informal assessments, I move amongst my students to see what they
are doing mathematically (and for behavior management), ...my demo lesson
should reflect what I do.
I wish I could be of more help.
-Jeanne, for the Teacher2Teacher service